The following two rules will fix 99% of any mistakes you might be tempted to make with leading vs lagging power factor for the PE exam.

What’s in this article?

– Leading and Lagging Cheat Sheet:

1. Power Angle Rule #1

For a three-phase or single-phase system, the power angle (θ) of the circuit will always be equal to the impedance angle (θz):

2. Power Angle Rule #2

The phase current angle (θIp) is equal to the power angle (θ) except opposite in polarity when zero degrees is used as the reference angle for the phase voltage (θVp):

3. Lagging Power Factor Diagrams

A lagging power factor means the impedance in the circuit is inductive and causing the phase current to lag the phase voltage.
This means our phase current has a negative angle when the phase voltage is at 0º.
Let’s look at our phasor diagram for phase current and phase voltage, and let’s look at our power triangle for complex power when our phase voltage is at a reference of 0 degrees:

For a lagging power factor, the phase current always lags the phase voltage and the power angle theta (θ) is positive.

4. Leading Power Factor Diagrams

A leading power factor means the impedance of the circuit is capacitive and causing the phase current to lead the phase voltage.
This means our phase current has a positive angle when the phase voltage is at 0º.
Let’s look at our phasor diagram for phase current and phase voltage, and let’s look at our power triangle for complex power when our phase voltage is at a reference of 0 degrees:

For a leading power factor, the phase current always leads the phase voltage and the power angle theta (θ) is negative.

5. Lagging Power Factor Example

A three-phase, wye connected generator rated for 55 MVA and 13.8 kV is operating at full load with a 0.82 lagging power factor. Determine the complex line current delivered to the connected system using a reference of zero degrees for the system phase voltage.
We’ll use the three-phase apparent power |S3ø| formula and set it equal to current to solve for the line current (IL) of the system. For wye connections, line current (IL) and phase current (Ip) are equal, so we will use the result of this formula for the phase current to help us determine the angle for the complex current.
Since we are using a reference of zero degrees for the system phase voltage (Vp, or VLn), we will set the phase current angle (θIp) equal to the power angle (θ) and make the polarity negative (rule #2 above).

6. Leading Power Factor Example

A three-phase, wye connected generator rated for 55 MVA and 13.8 kV is operating at full load with a 0.82 leading power factor. Determine the complex line current delivered to the system using a reference of zero degrees for the system phase voltage.
We’ll use the three-phase apparent power |S3ø| formula and set it equal to current to solve for the line current (IL) of the system. For wye connections, line current (IL) and phase current (Ip) are equal, so we will use the result of this formula for the phase current to help us determine the angle of the complex current.
Since we are using a reference of zero degrees for the system phase voltage (Vp, or VLn), we will set the phase current angle (θIp) equal to the power angle (θ) and make the polarity positive (rule #2 above).

Notice the only variable we changed in each of the above examples is the power factor. The first example has a lagging power factor while the second example has a leading. All other variables in the problem were equal.

The only difference this resulted in is changing the polarity of both the power angle and the current angle.

7. Print for Reference

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Enjoy.